Well, there's loads of stuff not present in Unicode (though new characters are still being added).

Some examples:

• Due to Han Unification, Unicode uses one codepoint for several similar characters from different languages. People disagree whether these characters are really "the same"; if you believe they should be represented separately, then these separate representations could be said to be "missing" (though this is something of a philosophical question).
• In a similar vein, many languages (especially Asian languages) sometimes have several variants of one character/glyph. The distinction between "one character with several representations" (=one codepoint) and "distinct characters" (=different codepoints) is somewhat arbitratry, thus there are cases (e.g. with Kanji characters) where some people feel alternative variants are "missing".
• Many historic and rarely used characters are missing.
• Many old/historic scripts are not covered, e.g. Demotic. Actually, there is an initiative specifically for including more scripts in Unicode, the Script Encoding Initiative(SEI).

There is also a page by the W3C on this topic, Missing characters and glyphs, with more explanations.

..., as I can't tell where each plane ends.

Every plane by definition ends at U+xxFFFF.

On Unicodes website it refers to the last two characters of every plane being non characters.

No. The Unicode Standard Version 9.0 - Core Specification says (in section 23.7 Noncharacters):

The Unicode Standard sets aside 66 noncharacter code points. The last two code points of each plane are noncharacters: U+FFFE and U+FFFF on the BMP, U+1FFFE and U+1FFFF on Plane 1, and so on, up to U+10FFFE and U+10FFFF on Plane 16, for a total of 34 code points. In addition, there is a contiguous range of another 32 noncharacter code points in the BMP: U+FDD0..U+FDEF. For historical reasons, the range U+FDD0..U+FDEF is contained within the Arabic Presentation Forms-A block, but those noncharacters are not “Arabic noncharacters” or “right-to-left noncharacters,” and are not distinguished in any other way from the other noncharacters, except in their code point values.

Note the keyword "code points", not "characters", they are always U+xxFFFE and U+xxFFFF.